Structural batteries, devices that store energy and provide structural integrity, offer a viable solution to achieve mass savings in electric automobiles and aerospace vehicles. A structural battery electrolyte (SBE) is a vital component in structural batteries that facilitates ion transport and mechanical load transfer simultaneously. SBEs combine liquid electrolyte and mechanically robust materials into a bicontinuous structure. There is an intrinsic tradeoff between effective mechanical and transport properties of SBEs. These effective properties are influenced by the SBE microstructure, the properties of the SBE constituents, and temperature. Proper material selection and precise control of the SBE microstructure is necessary to attain desirable transport and mechanical performance at different temperatures. The present work develops a finite element model for an SBE, analyzes the magnitude of the tradeoff, and studies the effective elastic modulus and ionic conductivity as a function of composition, microstructure, and temperature. The results are compared to classical models, including mean-field micromechanics for elastic modulus and ionic conductivity and the Bruggeman correction for ionic conductivity. In future work, new SBE microstructure designs with shorter ion pathways and improved mechanical performance for additive manufacturing will be proposed.